It seems to be random. I got it after only maybe 10 plays, but didn't get another jackpot for a while. Just keep trying.
As with the slot machines in BioShock, this is a matter of random chance. The first time you use a slot machine in BioShock 2 you are guaranteed to win a $25 prize. After that the chance of winning greatly decreases. So to get the jackpot, just keep pulling the lever, the pay-out is $250 for both games.
Factoid: The first time Booker plays a machine in Burial at Sea, Elizabeth will comment, “Best quit while you’re ahead.” Then the machine will stop on 7-7-☆, 77 is the number of the winning ball, Mr. Dewitt chooses at the Raffle square, Columbia in BioShock Infinite.